Partially Inelastic Collision

Q.

A body of mass $m_1$ collides elastically with another body of mass $m_2$ at rest. If the velocity of $m_1$ after collision becomes$\frac{2}{3}$ times its initial velocity, the ratio of their masses is

1. $1:5$

2. $5:1$

3. $5:2$

4. $2:5$

Q.

Two identical blocks A and B of mass M each are kept on each other on a smooth horizontal plane. There exists friction between A and B. If a bullet of mass m hits the lower block with a horizontal velocity v and gets embedded into it, the work done by friction between A and B is

1. - $\frac{M{m}^2{v}^2}{2(m+2M)(m+M)}$

2. - $\frac{M{m}^2{v}^2}{(m+2M)(m+2M)}$

3. - $\frac{M{m}^2{v}^2}{2(m+2M)(m+M)}$

4. - $\frac{M{m}^2{v}^2}{2(m+2M)(2m+M)}$

Q.

A block of mass 1.2 kg moving at a speed of 20 cm/s collides head-on with a similar block kept at rest. The coefficient of restitution is $\frac{3}{5}$. Find the loss of kinetic energy during the collision.

1. 7.7 × 10^-2 J

2. 7.7 × 10^-1 J

3. 7.7 × 10^-3 J

4. 7.7 × 10^-4 J

Q. Are the given formulas correct for inelastic collision? v1= ev1[(m1-m2)/(m1+m2)] + [(1+e)v2m2/(m1+m2)] v2= ev2[(m2-m1)/(m1+m2)] + [(1+e)v1m1/(m1+m2)] where e=coefficient of restitution

Q. A metal ball falls from a height of $1\text{m}$ on a steel plate and jumps upto a height of $81\text{cm}$. Find the coefficient of restitution for the collision.

1. $0.7$
2. $0.8$
3. $0.6$
4. $0.9$

Q.

A ball is projected with a velocity $u$ at an elevation from a point distance d from a smooth vertical wall in a plane perpendicular to it. After rebounding from the wall, it returns to the point of projection, find the maximum distance $d$ for which the ball can return to the point of projection.

1. 

2. 

3. 

4. 

Q.

A ball hits the floor and rebounds after inelastic collision. In this case

1. The mechanical energy of the ball remains the same in the collision

2. The total energy of the ball and the earth is conserved

3. The total momentum of the ball and the earth is conserved

4. The momentum of the ball just after the collision is the same as that just before the collision

Q.

A lead ball strikes a wall and falls down, a tennis ball having the same mass and velocity strikes the wall and bounces back. Check the correct statement

1. The momentum of the lead ball is greater than that of the tennis ball

2. The lead ball suffers a greater change in momentum compared with the tennis ball

3. The tennis ball suffers a greater change in momentum as compared with the lead ball

4. Both suffer an equal change in momentum

Q. If a particle is moving along y =x+4 in xy plane . Its velocity is v and mass is m . Its angular momentum about origin is?

Q. A ball is moving with a speed of $4\text{m/s}$ towards a heavy wall. The wall is also moving towards the ball with velocity of $1\text{m/s}$. If the coefficient of restitution is $0.5$, find the velocity of the ball immediately after the collision. (Assume that the wall maintains the same speed even after the collision.)

1. $3.5\text{m/s}$ along initial direction.
2. $1.5\text{m/s}$ opposite to initial direction.
3. $2.5\text{m/s}$ opposite to initial direction.
4. $3.5\text{m/s}$ opposite to initial direction.

Q.

A ball drops from the ceiling of the room, and after rebounding twice from the floor, reaches a height equal to half that of ceiling. Find the coefficient of restitution?

1. $\sqrt{\frac{1}{2}}$

2. $\frac{1}{2}$

3. $4\sqrt{\frac{1}{2}}$

4. $3\sqrt{\frac{1}{2}}$

Q.

A ball of mass ${}^{\prime }{m}^{\prime }$ moving horizontally which velocity ${}^{\prime }{u}^{\prime }$ hits a wedge of mass ${}^{\prime }{M}^{\prime }$. the wedge is situated on a smooth horizontal surface. If after striking wedge the ball starts moving in vertical direction and the wedge starts moving in horizontal plane. Calculate the coefficient of restitution $e$.

1. $\frac{M}{m}+ta{n}^2\theta$

2. $\frac{m}{M}+co{t}^2\theta$

3. $\frac{m}{M}+ta{n}^2\theta$

4. $\frac{M}{m}+co{t}^2\theta$

Q. why if the kinetic engy of a sytem is zero impkies(implies) its line momentum is also zsero(zero)?

Q. In the figure shown below, a ball is moving with a velocity of $u_1=7\text{m/s}$ in downward direction towards a surface, while the surface is moving in upward direction with a constant velocity $u_2=3\text{m/s}$. If the coefficient of restitution has value of $e=0.8$ and after collision with the surface, the ball rebounds back with velocity $v\text{m/s}$, find the rebound velocity. (Neglect all external forces)

1. $5\text{m/s upward}$
2. $11\text{m/s downward}$
3. $11\text{m/s upward}$
4. $5\text{m/s downward}$

Q. A particle strikes a horizontal smooth floor with a velocity $u$ making an angle $\theta$ with the floor and rebounds with velocity $v$ making an angle $\varphi$ with the floor. If the coefficient of restitution between the particle and the floor is $e$, then

1. the impulse delivered by the floor to the body is $mu(1+e)\sin \theta$.
2. $\tan \varphi =e\tan \theta$
3. $v=u\sqrt{1-(1-e^2){\sin }^2\theta }$
4. The ratio of the final kinetic energy to the initial kinetic energy is $({\cos }^2\theta +e^2\sin \theta )$

Q. If the earth reduces its radius by half, what would be the duration of day?

Q. A particle is dropped from a height $h$ on a floor, if the coefficient of restitution is $e$. Find the time taken by ball before second bounce.

1. $\sqrt{\frac{2h}{g}}(2+e)$
2. $\sqrt{\frac{2h}{g}}(1+e)$
3. $\sqrt{\frac{2h}{g}}(1+\frac{2}{e})$
4. $\sqrt{\frac{2h}{g}}(1+2e)$